NEURAL NETWORKS AND COMBINATORIAL OPTIMIZATION PROBLEMS --- THE KEY TO A SUCCESSFUL MAPPING
Andrew H. Gee, Sreeram V. B. Aiyer and Richard W. Prager
For several years now there has been much research interest in the use of Hopfield networks to solve combinatorial optimization problems. Although initial results were disappointing, it has since been demonstrated how modified network dynamics and better problem mapping can greatly improve the solution quality. The aim of this paper is to build on this progress by presenting a new analytical framework in which problem mappings can be evaluated without recourse to purely experimental means. A linearized analysis of the Hopfield network's dynamics forms the main theory of the paper, followed by a series of experiments in which some problem mappings are investigated in the context of these dynamics. In all cases the experimental results are compatible with the linearized theory, and observed weaknesses in the mappings are fully explained within the framework. What emerges is a largely analytical technique for evaluating candidate problem mappings, without having to resort to the more usual trial and error.
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